The Dirichlet Boundary Value Problem in Strongly Perforated Domains with Complex Boundary
In this chapter, we study the asymptotic behavior of solutions of the Dirichlet problem in domains ω(s)=ω/F (s) , where ω is some fixed domain in ℝ n (n≥2) and F (s) (s=1, 2,…) are arbitrary closed sets. In contrast with the preceding chapter, where the sets F (s) =U i=1 s F i (s) consisting of disjoint components F i (s) , “grains,” have been considered, here the main attention is focused on connected sets F (s) . Typically, such sets consist of thin (generally, intersecting) fibers forming weblike structures.
KeywordsVariational Problem Dirichlet Problem Weak Limit Orlicz Space Complex Boundary
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